Given that In five years time job will be four times as old as his son Mark and Two years ago Jon was eleven times as old as mark.
Let the age of job and mark now be x and y years old.
So, in five years the age of job will be x + 5 and the age of his son mark will be y + 5.
According to the question,
[tex]\begin{gathered} x+5=4(y+5) \\ x+5=4y+20 \\ x-4y=15 \end{gathered}[/tex]Two years ago, the age of job was x - 2 and the age of his son mark was y - 2.
So, according to the question.
[tex]\begin{gathered} x-2=11(y-2) \\ x-2=11y-22 \\ x-11y=-20 \end{gathered}[/tex]From the first equation, we have x = 4y + 15. Substitute this value in the second equation and solve:
[tex]\begin{gathered} 4y+15-11y=-20 \\ -7y=-35 \\ y=5 \end{gathered}[/tex]Substitute y = 5 in x = 4y + 15.
[tex]\begin{gathered} x=4(5)+15 \\ x=20+15 \\ x=35 \end{gathered}[/tex]Thus, the present age of job is 35 years and the present age of his son mark is 5 years.
Find a.Round to the nearest tenth:2 cmс1501050a=a = [ ? ]cmLaw of Sines: sin A=sin Bb=sin Cсa
In the given triangle ABC ,
Sum of the angles of of a triangle is 180 degrees.
Therefore,
[tex]\begin{gathered} \angle A\text{ + }\angle B\text{ + }\angle C\text{ = 180} \\ \angle A\text{ + 105 + 15 = 180} \\ \angle A=\text{ 180 - 120} \\ \angle A\text{ = 60} \end{gathered}[/tex]By using sine rule,
[tex]\frac{a}{\sin A}\text{ = }\frac{b}{\sin B}[/tex]Substituting the given values in the given equation,
[tex]\begin{gathered} \frac{a}{\sin60}\text{ = }\frac{2}{\sin 105} \\ a\text{ = }\frac{2\sin 60}{\sin 105} \\ a\text{ = 1.7931 } \\ a\text{ }\approx\text{ 1.8 }cm \end{gathered}[/tex]In a game, a spinner with 8 equally sized sections numbered 1 to 8 is spun and a die is tossed. What is the probability of landing on an odd number on the spinner and rolling aneven number on the die?
ANSWER
1/4
EXPLANATION
The spinner has 8 equally sized sections numbered 1 to 8.
The die has 6 faces.
On the spinner there are 4 sections with odd numbers and 4 sections with even numbers.
On a die, there are 3 faces with even numbers and 3 faces with odd numbers.
To find the probability of both events occuring, we need to find their individual probabilities and then multiply them together.
The probability of landing on an odd number on the spinner is:
4/8 i.e. 1/2
The probability of rolling an even number on the die is:
3/6 i.e. 1/2
Therefore, the probability of landing on an odd number on the spinner and rolling an even number on the die is:
[tex]\begin{gathered} \frac{1}{2}\cdot\text{ }\frac{1}{2} \\ \text{= }\frac{1}{4} \end{gathered}[/tex]y-(-4)= x-(-5)what is y
What is the ratio of all the apples in the bag to red and green ?
There are 11 apples on the basket, if 5 of them are green and the rest are red, to determine the number of red apples, you have to calculate the difference between the total and the number of green apples:
[tex]11-5=6[/tex]a) There are 6 red apples on the basket, the ratio of all apples to red apples can be expressed as follows:
First, write the total number of apple and then write the number of red apples, separate both values by a colon
[tex]11\colon6[/tex]b) To write the ratio of red apples to green apples you have to write the number of red apples on the basket and the number of green apples, both values separated by a colon:
[tex]6\colon5[/tex]Francis went on a business trip to Minneapolis, Minnesota, and stayed at a hotel for one night at a rate of $150, plus tax. The state of Minnesota has a general sales tax rate of 6.875%, and the city of Minneapolis has a general sales tax rate of 0.5%. In addition, Hennepin County, where Minneapolis is located, has a 0.25% sales tax for transit improvement and a 0.15% sales tax to finance a baseball stadium. Not only that, but there is an additional lodging tax in Minneapolis of 3%. Help Francis determine his total bill at the hotel. Round all your answers to the nearest cent. How much money was Francis charged by the state of Minnesota at its general sales tax rate?How much money was Francis charged by the city of Minneapolis at its general sales tax rate? How much money was Francis charged by Hennepin County for transit improvement? How much money was Francis charged by Hennepin County to help finance a baseball stadium?
Francis went on a business trip to Minneapolis, Minnesota, and stayed at a hotel for one night at a rate of $150, plus tax. The state of Minnesota has a general sales tax rate of 6.875%, and the city of Minneapolis has a general sales tax rate of 0.5%. In addition, Hennepin County, where Minneapolis is located, has a 0.25% sales tax for transit improvement and a 0.15% sales tax to finance a baseball stadium. Not only that, but there is an additional lodging tax in Minneapolis of 3%. Help Francis determine his total bill at the hotel. Round all your answers to the nearest cent.
How much money was Francis charged by the state of Minnesota at its general sales tax rate?
How much money was Francis charged by the city of Minneapolis at its general sales tax rate?
How much money was Francis charged by Hennepin County for transit improvement?
How much money was Francis charged by Hennepin County to help finance a baseball stadium?
part 1How much money was Francis charged by the state of Minnesota at its general sales tax rate?
we have that
the sales tax rate is 6.875%
6.875%=6.875/100=0.06875
Multiply by $150
150(0.06875)=$10.31
part 2How much money was Francis charged by the city of Minneapolis at its general sales tax rate?
the sales tax rate is 0.5%
0.5=0.5/100=0.005
Multiply by $150
150(0.005)=$0.75
part 3How much money was Francis charged by Hennepin County for transit improvement?
sales tax is 0.25%
0.25/100=0.0025
150(0.0025)=$0.38
part 4How much money was Francis charged by Hennepin County to help finance a baseball stadium?
the sales tax is 0.15%
0.15/100=0.0015
150(0.0015)=$0.23
part 5additional lodging tax in Minneapolis of 3%
3/100=0.03
150(0.03)=$4.5
part 6
the total bill is equal to
150+10.31+0.75+0.38+0.23+4.5=$166.17
the total bill is $166.17What is the first step to solve 1/4x- 5=8
Given the equation :
[tex]\frac{1}{4}x-5=8[/tex]The first step is to add 5 to both sides
so,
[tex]\frac{1}{4}x-5+5=8+5[/tex]Write a quadratic equation in factored form if it has x-intercepts 2 and -1 and y-intercept 6.
We have to write a quadratic equation, in factored form, that has an x-intercept at x=2 and x=-1, and a y-intercept 6.
As the x-intercepts are the roots of the function, we can write the equation as:
[tex]y=a(x-2)(x+1)[/tex]The parameter a will be defined in order to have a y-intercept at y=6. That means that, when x is 0, the value of the function is y=6.
Then, we can replace x with 0 and y with 6 and find the value of a:
[tex]\begin{gathered} y=a(x-2)(x+1) \\ 6=a(0-2)(0+1) \\ 6=a(-2)(1) \\ 6=-2a \\ a=\frac{6}{-2} \\ a=-3 \end{gathered}[/tex]With the value of a=-3, we can write the factorized form of the equation as:
[tex]y=-3(x-2)(x+1)[/tex]Graph:
Answer: y=-3(x-2)(x+1)
3) Select all ratios that are equivalent to 4:5 A. 2: 2.5 B. 2:3 C. 3: 3.75 D. 7:8 E. 8:10 F. 14: 27.5
For two ratios to be equivalent, its means and extremes if multiplied must be equal to each other.
[tex]\begin{gathered} \frac{a}{b}=\frac{c}{d} \\ ad=bc \end{gathered}[/tex]Let's start with Option A.
[tex]\begin{gathered} \frac{4}{5}=\frac{2}{2.5} \\ 4\times2.5=2\times5 \\ 10=10 \end{gathered}[/tex]Since they are equal, then Option A is equivalent to 4/5.
Let's check Option B.
[tex]\begin{gathered} \frac{4}{5}=\frac{2}{3} \\ 4\times3=2\times5 \\ 12\ne10 \end{gathered}[/tex]Let's check Option C.
[tex]\begin{gathered} \frac{4}{5}=\frac{3}{3.75} \\ 4\times3.75=5\times3 \\ 15=15 \end{gathered}[/tex]Let's check Option D.
[tex]\begin{gathered} \frac{4}{5}=\frac{7}{8} \\ 4\times8=5\times7 \\ 32\ne35 \end{gathered}[/tex]Let's check Option E.
[tex]\begin{gathered} \frac{4}{5}=\frac{8}{10} \\ 4\times10=5\times8 \\ 40=40 \end{gathered}[/tex]FInally, let's check Option F.
[tex]\begin{gathered} \frac{4}{5}=\frac{14}{27.5} \\ 4\times27.5=5\times14 \\ 110\ne70 \end{gathered}[/tex]Hence, only Option A, Option C, and Option E are equivalent to ratio 4/5.
which of the following values are solutions to the inequality -6<-7-4x?1. 12. -83. 5or none
The Solution:
Given:
Required:
Find f(2):
[tex]\begin{gathered} f(2)=\sqrt{[(-5\times2)+14]}=\sqrt{-10+14}=\sqrt{4}=2 \\ \\ f(2)=2 \end{gathered}[/tex]Find g(-5):
[tex]\begin{gathered} g(-5)=\frac{-5}{(-5)^2-7}=\frac{-5}{25-7}=-\frac{5}{18} \\ \\ g(-5)=-\frac{5}{18} \end{gathered}[/tex]Find h(-1/2):
[tex]\begin{gathered} h(-\frac{1}{2})=|6(-\frac{1}{2})|-9=|-3|-9=3-9=-6 \\ \\ h(-\frac{1}{2})=-6 \end{gathered}[/tex]Answer:
f(2) =
[tex]-6<-7-4x[/tex]now we can solve the inequalty for x by passing the -7 to the other side:
[tex]\begin{gathered} 7-6<-4x \\ 1<-4x \end{gathered}[/tex]Now to change the sign of the -4x we have to invert the inequality:
[tex]\begin{gathered} -1>4x \\ \frac{-1}{4}>x \end{gathered}[/tex]so the only solution is -8 and we can prove it:
[tex]-6<-7-4(-8)[/tex]In Mr. Senter's classroom, 2/3 of the students play sudoku. Of the students who play sudoku, 3/8 also play chess. If there are 24 students in his class, how many play sudoku and chess?how did she get 9
The number of students given are 24.
The students who play sudoku is,
[tex]\frac{2}{3}\times24=16.[/tex]Out of the students who play sudoku , the students who play chess are
[tex]16\times\frac{3}{8}=6.[/tex]Therefore the students who play sudoku are 16 and play chess are 6.
The number of students who play both chess and sudoku is,
[tex]\text{ n}(C\cup S)=n(C)+n(S)-n(C\cap S)[/tex]Substitute the values,
[tex]24=16+6-n(C\cap S)[/tex][tex]n(C\cap S)=24-22[/tex][tex]n(C\cap S)=2.[/tex]Thus , the number of students who play both chess and sudoku is, 2.
what is the degree of the polynomial5z^3-2z^4-9z^2+z
The degree of a polynomial is the highest power in the inividual terms
Hence the degree of this polynomial is 4
Raul works at a movie theatre. The function f(x) represents the amount of money Raul earns per ticket, where x is the number of tickets he sells. The function g(x) represents the number of tickets Raul sells per hour, where x is the number of hours he works. Show all work to find f(g(x))f(x) = 2x2 + 16g(x) = /5x^3
Given the functions
[tex]\begin{gathered} f(x)=2x^2+16 \\ g(x)=\sqrt[]{5x^3} \end{gathered}[/tex]First, we get the composite function
[tex]f(g(x))=f(\sqrt[]{5x^3})[/tex]To get f(√5x³), we will substitute x in f(x) with √5x³ as shown:
[tex]f(g(x))=2(\sqrt[]{5x^3})^2+16[/tex]The square root and power 2 cancel each other
[tex]\begin{gathered} f(g(x))=2(5x^3)+16 \\ \text{Simplify} \\ f(g(x))=10x^3+16 \end{gathered}[/tex]Answer:
[tex]f(g(x))=10x^3+16[/tex]Solve 5x + 6 = 7 for x.
x = 1/5
Explanations:The given equation is:
5x + 6 = 7
Step 1: Collect like terms
Note that 6 becomes -6 when it crosses to the right side of the equality sign
5x = 7 - 6
5x = 1
Step 2: Divide both sides by 5
5x / 5 = 1 / 5
x = 1 / 5
write the function value in term of the cofunction of a complementary angle .
Answer:
Explanations:
Note that the secant and cosecant functions are cofunctions and are also complements.
Therefore, they are related mathematically as:
csc x = sec ( 90° - x)
x = 64°
csc 64° = sec (90° - 64°)
csc 64° = sec 26
Four students tried to create factor rainbows for the number 81. Complete the statements below about the number 81.
3⁴ is factor rainbows for the number 81.
What does a math factor mean?
A number that divides another number by itself with no residual is known as a factor. In other words, if multiplying two whole numbers results in the creation of a product, the numbers we are multiplying are factors of the product since the product is divisible by them.81 is a perfect square number.
Hence, we can express it as 9 × 9 = 81.
9 can further be factored as 3 × 3 = 9.
Factor of 81 = 1,3,9,27,81
negative factor of 81 = -1,-3,-9,-27,-81
prime factors of 81 = 3 * 3 * 3 * 3 = 3⁴
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Consider the following data:x-2-1 0 1P(X=x) 0.10.10.20.2Step 4 of 5: Find the value of P(X < 2). Round your answer to one decimal place.20.4
STEP - BY - STEP EXPLANATION
What to find?
P(X < 2)
Given:
[tex]P(X<2)=P(X=-2)+P(X=-1)+P(X=0)+P(X=1)[/tex]From the given table;
P(X=-2) = 0.1
P(X=-1)=0.1
P(X=0)=0.2
P(X=1)=0.2
Substitute the values into the formula above and simplify.
[tex]P(X<2)=0.1+0.1+0.2+0.2[/tex][tex]=0.6[/tex]Hence, P(X < 2)=0.6
ANSWER
0.6
evaluate the expression 4-2i/3i
and write the result in the form a+bi
The given expression in the form of (a + ib) can be written as -
-2/3 + i(4/3).
What is a expression? What is a mathematical equation? What is Equation Modelling? What are complex numbers?A mathematical expression is made up of terms (constants and variables) separated by mathematical operators. A mathematical equation is used to equate two expressions. Equation modelling is the process of writing a mathematical verbal expression in the form of a mathematical expression for correct analysis, observations and results of the given problem. In mathematics, a complex number is an element of a number system that extends the real numbers with a specific element denoted [i], called the imaginary unit and satisfying the equation -
[tex]{\displaystyle i^{2}=-1}[/tex]
Every complex number can be expressed in the form a + bi, where [a] and [b] are real numbers
We have the following expression -
(4 - 2i)/3i
We have -
(4 - 2i)/3i
4/3i - 2i/3i
- 2/3 + i(4/3)
Therefore, the given expression in the form of (a + ib) can be written as -
-2/3 + i(4/3).
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Which of the following illustratesthe associative property ofmultiplication?Enter a, b, c, d, or e.(a + b)(cd) =a. acd + bcdb. (b + a)(cd)c. (ac + bc)d d. [(a + b)c]de. (cd)(a + b)
The associative property of multiplication states that
[tex](a\cdot b)\cdot c=a\cdot(b\cdot c)[/tex]Given that (a+b)(cd), then its associative counterpart is
[tex](a+b)\mleft(cd\mright)=\lbrack(a+b)c\rbrack d[/tex]Can you help me understand how to do this please?
The given equation is
- 26 = 2(u - 7) - 8u
The first step is to expand the parentheses on the right side of the equation by multiplying the terms inside by the term outside. We have
- 26 = 2u - 14 - 8u
The next step is to collect like terms. The terms containing u will be on one side of the equation while the constant terms would be on the other side.
By adding 14 to both sides of the equation, we have
- 26 + 14 = 2u - 14 + 14 - 8u
- 12 = 2u - 8u
- 12 = - 6u
- 6u = - 12
Dividing both sides of the equation by - 6, we have
- 6u/- 6 = - 12/- 6
u = 2
I need help with this problem pleaseAfter number it says number of visits
The inequality: 2.5v + 20 ≥ 40
v ≥ 8
Explanation:Rewards for signing up = 20
let the number of visits = v
rate = 2.5 points per visit
Amount needed for a free movie ticket is atleast 40 points
Atleast 40 is reperesented as ≥ 40
Rewards for signing up + rate (number of visits) ≥ 40
20 + 2.5(v) ≥ 40
The inequality:
2.5v + 20 ≥ 40
Solving the inequality:
2.5v + 20 - 20 ≥ 40 - 20
2.5v ≥ 20
v ≥ 20/2.5
v ≥ 8
What is the y-intercept of function f? f(x)={-3x-2, -infinity
======================================================
Explanation:
The y intercept always occurs when x = 0.
Visually this is where the function curve crosses or touches the vertical y axis.
The input x = 0 fits into the interval [tex]-2 \le \text{x} < 3[/tex] since [tex]-2 \le 0 < 3[/tex] is a true statement. This means we'll go for the second piece of the piecewise function.
Plug x = 0 into this middle piece to get...
f(x) = -x+1
f(0) = -0+1
f(0) = 1
Describe the net of a rectangular prism with a length of 12 centimeters a width of 9 centimeters and height of 5.
There would be a line of 4 rectangles, and 2 rectangles on the top and bottom of the second one. The first and third rectangles would have a width of 12, and the first and fourth would have a width of 9.
The rectangles on the top and bottom would also have a width of 9. The 4 rectangles would have a height of 5, and the 2 rectangles on the top and bottom would have a height of 12.
i need to solve c pls help were working on on srthemic sequence formula sn=n/2(u1+un)
Answer: 78,800
The formula is given as
Sn = n/2(u1 + Un)
Let n = 16
u1 = first term
Un = Last term
According to the table given
U1 = 6800
U16 = 3050
S16 = 16/2( u1 + u16)
S16 = 16/2(6800 + 3050)
Firstly, solve the expression inside the parenthesis
S16 = 16/2 (9850)
S16 = 8 x 9850
S16 = 78,800
The answer is 78,800
TS and TV are tangent to circle P. What is the value of x?
tangent = tangent
x^2-1 = 24
Add 1 to each side
x^2 -1 +1 = 24+1
x^2 = 25
Take the square root of each side
sqrt(x^2) = sqrt(25)
x = 5
x cannot be negative, because distances cannot be negative
Fernando picks a marble at random. without putting the first marble back he picks second marble at random are thertwo events dependent or independent
Given the word problem, we can deduce the following information:
1. Fernando picks a marble at random.
2. Without putting the first marble back, he picks a second marble at random.
To determine if the events are dependent or independent, we first note that dependent events influence the probability of other events, while independent events do not affect one another.
Since Fernando picks a marble without putting the first marble back, the probability of the second pick is affected.
Therefore, the answer is dependent.
A square window has an area of x² + 12x + 36 square feet. Find the length of oneside of the square
Solution
Given that a square window has an area of x² + 12x + 36
[tex]\begin{gathered} Area\text{ of square = l}^2 \\ Where\text{ l = length of the square} \\ Thus,\text{ length of the square= }\sqrt{Area}\text{ of the square} \end{gathered}[/tex][tex]\begin{gathered} l=\sqrt{x²+12x+36} \\ l=\sqrt{(x^2+6x+6x+36}) \\ l=\sqrt{x(x+6)+6(x+6)} \\ l=\sqrt{(x+6)(x+6)} \\ l=\sqrt{(x+6)^2} \\ l=x+6 \end{gathered}[/tex]The length of one side of the square = x+6
Use the following statement to answer parts a) and b). Two hundred raffle tickets are sold for $3 each. One prize of $1000 is to be awarded. Winners do not have their ticket costs of $3 refunded to them. Raul purchases one ticket.a) Determine his expected value.b) Determine the fair price of a ticket.
Fom the question, the following can be derived:
Ticket price = $3
Winning price = $1000
Probability of winning (Pwin) = (1/200)
Probability of not winning (Ploss) = [1 - (1/200)] = 199/200
The net income if Raul wins (Nwin) = $1000 - $3 = $997 (when there is no refund)
The net loss if Raul does not win (Nloss) = -$3
(a) We are to determine his expected value:
To determine his expected value, we using this:
(Pwin * Nwin) + (Ploss * Nloss)
((1/200) * 997) + ((199/200) * -3)
4.985 - 2.985 = 2
The expected value is 2.
(b) We are also to determine the fair price of a ticket
To get the fair price of a ticket, we will add the cost of ticket and the expected value:
Cost of ticket + Expected value
3 + 2 = 5
Therefore, the fair price of a ticket is 5.
9) At Go and Shop, apples cost $3 each and oranges cost $2.50 each. Maggie bought three times as manyapples as she did oranges. If her total was $46, how many of each fruit did she buy?
We have:
Let x = number of apples
Let y = number of oranges
Maggie bought three times as many apples as she did oranges, this is:
x = 3y
$3 each apple
$2.50 each orange
Total cost $46
Then, we have the expression:
[tex]3x+2.50y=46[/tex]Next, solve the system of equations:
we replace x = 3y in the second equation
[tex]3(3y)+2.50y=46[/tex]And solve for y
[tex]\begin{gathered} 9y+2.50y=46 \\ 11.5y=46 \\ \frac{11.5y}{11.5}=\frac{46}{11.5} \\ y=4 \end{gathered}[/tex]Therefore, x is:
[tex]undefined[/tex]2 step equations solve each equation. Show yourselves steps -18=6a-6x/-3 + 11 =233+2v=1116=k/3 - 11 -6g -12 = -602a+5-5a+1 combine like terms m-4+3m-2 combine like terms
In this case, we'll have to carry out several steps to find the solution.
Step 01:
Data
-18=6a-6
a = ?
Step 02:
-18 = 6a - 6
-18 + 6 = 6a
- 12 = 6a
-12 / 6 = a
- 2 = a
The answer is:
a = - 2
Solve the following system of equations by using elimination: x + 2y = 8 -x - 3y = 2
Solve the following system of equations by using elimination:
[tex]\begin{cases}x+2y=8\ldots\ldots\text{.}(1) \\ -x-3y=2\ldots\ldots(11)\end{cases}[/tex]Using Elimination method:
[tex]\begin{gathered} \begin{cases}x+2y=8 \\ \frac{-x-3y=2}{-y=10}\end{cases}\text{+} \\ \text{divide both side by -1} \\ -\frac{y}{-1}=\frac{10}{-1} \\ y=-10 \end{gathered}[/tex]Substitute the value of y in equation (1):
[tex]\begin{gathered} x_{}+2y=8 \\ x+2(-10)=8 \\ x-20=8 \\ x=8+20 \\ x=28 \end{gathered}[/tex]Therefore the value of x = 28 and y = -10
Hence the correct answer is (x,y) = (28,-10)